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Reference Guide
Fibonacci.C File Reference

Detailed Description

View in nbviewer Open in SWAN A TH2Poly build with Fibonacci numbers.

In mathematics, the Fibonacci sequence is a suite of integer in which every number is the sum of the two preceding one.

The first 10 Fibonacci numbers are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

This tutorial computes Fibonacci numbers and uses them to build a TH2Poly producing the "Fibonacci spiral" created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling.

void Arc(int n, double a, double r, double *px, double *py);
void AddFibonacciBin(TH2Poly *h2pf, double N);
void Fibonacci(int N=7) {
// N = number of Fibonacci numbers > 1
TCanvas *C = new TCanvas("C", "C", 800, 600);
C->SetFrameLineWidth(0);
TH2Poly *h2pf = new TH2Poly(); // TH2Poly containing Fibonacci bins.
h2pf->SetTitle(Form("The first %d Fibonacci numbers",N));
h2pf->SetMarkerColor(kRed-2);
h2pf->SetStats(0);
double f0 = 0.;
double f1 = 1.;
double ft;
AddFibonacciBin(h2pf, f1);
for (int i=0; i<=N; i++) {
ft = f1;
f1 = f0 + f1;
f0 = ft;
AddFibonacciBin(h2pf, f1);
}
h2pf->Draw("A COL L TEXT");
}
void Arc(int n, double a, double r, double *px, double *py) {
// Add points on a arc of circle from point 2 to n-2
double da = TMath::Pi()/(2*(n-2)); // Angle delta
for (int i = 2; i<=n-2; i++) {
a = a+da;
px[i] = r*TMath::Cos(a) + px[0];
py[i] = r*TMath::Sin(a) + py[0];
}
}
void AddFibonacciBin(TH2Poly *h2pf, double N) {
// Add to h2pf the bin corresponding to the Fibonacci number N
double X1 = 0.; //
double Y1 = 0.; // Current Fibonacci
double X2 = 1.; // square position.
double Y2 = 1.; //
static int MoveId = 0;
static double T = 1.; //Current Top limit of the bins
static double B = 0.; //Current Bottom limit of the bins
static double L = 0.; //Current Left limit of the bins
static double R = 1.; //Current Right limit of the bins
const int NP = 50; // Number of point to build the current bin
double px[NP]; // Bin's X positions
double py[NP]; // Bin's Y positions
double pi2 = TMath::Pi()/2;
switch (MoveId) {
case 1:
R = R+N;
X2 = R;
Y2 = T;
X1 = X2-N;
Y1 = Y2-N;
px[0] = X1;
py[0] = Y2;
px[1] = X1;
py[1] = Y1;
px[NP-1] = X2;
py[NP-1] = Y2;
Arc(NP,3*pi2,(double)N,px,py);
break;
case 2:
T = T+N;
X2 = R;
Y2 = T;
X1 = X2-N;
Y1 = Y2-N;
px[0] = X1;
py[0] = Y1;
px[1] = X2;
py[1] = Y1;
px[NP-1] = X1;
py[NP-1] = Y2;
Arc(NP,0.,(double)N,px,py);
break;
case 3:
L = L-N;
X1 = L;
Y1 = B;
X2 = X1+N;
Y2 = Y1+N;
px[0] = X2;
py[0] = Y1;
px[1] = X2;
py[1] = Y2;
px[NP-1] = X1;
py[NP-1] = Y1;
Arc(NP,pi2,(double)N,px,py);
break;
case 4:
B = B-N;
X1 = L;
Y1 = B;
X2 = X1+N;
Y2 = Y1+N;
px[0] = X2;
py[0] = Y2;
px[1] = X1;
py[1] = Y2;
px[NP-1] = X2;
py[NP-1] = Y1;
Arc(NP,2*pi2,(double)N,px,py);
break;
}
if (MoveId==0) h2pf->AddBin(X1,Y1,X2,Y2); // First bin is a square
else h2pf->AddBin(NP, px ,py); // Other bins have an arc of circle
h2pf->Fill((X1+X2)/2.5, (Y1+Y2)/2.5, N);
MoveId++;
if (MoveId==5) MoveId=1;
}
Author
Olivier Couet

Definition in file Fibonacci.C.

n
const Int_t n
Definition: legend1.C:16
TH2Poly::AddBin
virtual Int_t AddBin(TObject *poly)
Adds a new bin to the histogram.
Definition: TH2Poly.cxx:222
TMath::Cos
Double_t Cos(Double_t)
Definition: TMath.h:643
Form
char * Form(const char *fmt,...)
r
ROOT::R::TRInterface & r
Definition: Object.C:4
N
#define N
TH1::SetTitle
virtual void SetTitle(const char *title)
See GetStatOverflows for more information.
Definition: TH1.cxx:6344
ROOT::Math::Cephes::C
static double C[]
Definition: SpecFuncCephes.cxx:187
TGeant4Unit::L
static constexpr double L
Definition: TGeant4SystemOfUnits.h:123
R
#define R(a, b, c, d, e, f, g, h, i)
Definition: RSha256.hxx:128
TMath::Pi
constexpr Double_t Pi()
Definition: TMath.h:43
a
auto * a
Definition: textangle.C:12
TMath::Sin
Double_t Sin(Double_t)
Definition: TMath.h:639
kRed
@ kRed
Definition: Rtypes.h:66
TGeant4Unit::pi2
static constexpr double pi2
Definition: TGeant4SystemOfUnits.h:76
TH1::SetStats
virtual void SetStats(Bool_t stats=kTRUE)
Set statistics option on/off.
Definition: TH1.cxx:8445
f1
TF1 * f1
Definition: legend1.C:11
TCanvas
Definition: TCanvas.h:23
ROOT::Math::Chebyshev::T
double T(double x)
Definition: ChebyshevPol.h:52
TH2Poly::Fill
virtual Int_t Fill(Double_t x, Double_t y)
Increment the bin containing (x,y) by 1.
Definition: TH2Poly.cxx:589
TH2Poly
Definition: TH2Poly.h:66
ROOT::Math::Cephes::B
static double B[]
Definition: SpecFuncCephes.cxx:178
TH1::Draw
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition: TH1.cxx:2997